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Interface Focus (2012) 2, 539–545
doi:10.1098/rsfs.2011.0120
Published online 7 March 2012
A look through ‘lens’ cubic
mitochondria
Zakaria Almsherqi1, Felix Margadant2 and Yuru Deng1, *
1
Cubic Membrane Research Laboratory, Department of Physiology, Yong Loo Lin School
of Medicine, National University of Singapore, Singapore
2
MechanoBiology Institute, National University of Singapore, Singapore
Cell membranes may fold up into three-dimensional nanoperiodic cubic structures in biological systems. Similar geometries are well studied in other disciplines such as mathematics,
physics and polymer chemistry. The fundamental function of cubic membranes in biological
systems has not been uncovered yet; however, their appearance in specialized cell types indicates a role as structural templates or perhaps direct physical entities with specialized
biophysical properties. The mitochondria located at the inner segment of the retinal cones
of tree shrew (Tupaia glis and Tupaia belangeri) contain unique patterns of concentric cristae
with a highly ordered membrane arrangement in three dimensions similar to the photonic
nanostructures observed in butterfly wing scales. Using a direct template matching
method, we show that the inner mitochondrial membrane folds into multi-layered (8 to 12
layers) gyroid cubic membrane arrangements in the photoreceptor cells. Three-dimensional
simulation data demonstrate that such multi-layer gyroid membrane arrangements in
the retinal cones of a tree shrew’s eye can potentially function as: (i) multi-focal lens;
(ii) angle-independent interference filters to block UV light; and (iii) a waveguide photonic
crystal. These theoretical results highlight for the first time the significance of multi-layer
cubic membrane arrangements to achieve near-quasi-photonic crystal properties through
the simple and reversible biological process of continuous membrane folding.
Keywords: gyroid; multi-layer cubic membranes; lens mitochondria;
cone photoreceptors; biophotonic crystals; interference filters
1. INTRODUCTION
gyroid (G), double diamond (D) and primitive (P) surfaces [3]. Cubic membranes have been observed in all
kingdoms of life, and they do not appear to be associated with any particular biomembrane, such as the
plasma membrane, endoplasmic reticulum, nuclear
envelope, chloroplasts or inner mitochondrial membrane. Although they have been observed in numerous
cell types and under different conditions, particularly
in stressed or diseased cells, knowledge about the
formation and function of such non-lamellar, cubic
structures in biological systems is scarce, and research
so far is restricted to the descriptive level. The frequent
appearance of cubic membranes in differentiated and
highly specialized cell types poses the intriguing question
as to their specific function(s). It is possible that cubic
membranes are but an inevitable self-assembled product
of the complex molecular mixture of the lipids and
proteins, the result of ‘simple’ molecular packing considerations and inter-molecular interactions. However,
an increasing body of evidence suggests that these structural organizations might have to fulfil a specific purpose
and their formation cannot be rationalized solely by
spontaneous molecular packing.
The mitochondria in the inner segment of the cone
photoreceptor of certain tree shrew species are unique
in size and ultrastructural arrangement of their inner
membranes [4]. The average size of mammalian
It is generally assumed that mitochondria are rather
homogeneous in their shapes and sizes localized throughout the cytoplasm. However, application of transmission
electron microscopy (TEM) and confocal microscopy for
visualization of mitochondria has established that the
structure of mitochondria in cells is highly dynamic.
The inner mitochondrial membrane arrangements may
vary from simple lamellar, tubular, vesicular, zigzag or
reticular structure to highly convoluted cubic membrane
arrangements [1,2]. The mechanisms underlying mitochondrial inner membrane organization and whether
this morphological heterogeneity is concomitant with
functional diversity remain unclear.
Cubic membrane arrangements represent highly
curved, three-dimensional nanoperiodic structures that
correspond to mathematically well-defined triply periodic minimal surfaces, or the corresponding periodic
nodal surfaces with constant mean curvature. So far,
three surface families have been identified to exist in
biological systems. They are designated according to
their corresponding triply periodic minimal surfaces as
*Author for correspondence ( [email protected]).
One contribution of 18 to a Theme Issue ‘Geometry of interfaces:
topological complexity in biology and materials’.
Received 1 December 2011
Accepted 10 February 2012
539
This journal is q 2012 The Royal Society
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540
Cubic lens mitochondria Z. Almsherqi et al.
(a)
(b)
(c)
Figure 1. Direct template-matching method to identify cubic membrane arrangements in transmission electron microscopy
(TEM) images (a) at the outer segment of the photoreceptor in tree shrew retina. Note the continuity of the inner mitochondrial
membrane organization across the apical mitochondrion and the adjacent mitochondria (encircled). The original TEM micrograph is from fig. 10 of Samorajski et al. [4], with permission (scale bar, 500 nm). (b) Three-dimensional level-surface plot of
the multi-layer gyroid cubic membrane arrangement; and (c) the corresponding computer-simulated two-dimensional projection
of a thick slice using the same gyroid model as (b). The TEM micrograph of lens mitochondria matches the theoretical projection
generated from multi-layer G-based level surfaces (+0.2, +0.4, +0.7, +0.9, +1.2) with 0.15 unit cell section thickness, viewed
from the lattice direction [h, k, l ] ¼ [9, 8, 1].
mitochondria is about 0.5 to 1 mm in diameter; however,
larger-sized mitochondria (about 5 mm in diameter)
have been reported in the retinal cones of at least two
mammals, Scandentia: common tree shrew (Tupaia
glis) [4] and northern tree shrew (Tupaia belangeri)
[5–7]. The retina of Tupaia is vastly different from
retina in other mammals and contains up to 95 per cent
cone cells, with only a few interspersed rods. In addition,
the inner segment of retinal cones of adult Tupaia contains several layers of mega-sized mitochondria (MG),
measuring 6–8 mm in diameter [4]. These mitochondria
contain a unique pattern of multi-layer cristae in a
highly ordered configuration (figure 1a). Although
these morphologically striking mitochondria have been
studied intensively in the past and some speculation
regarding their potential function in the photoreceptors
has been proposed [7], little work has been directed to
reveal their genuine three-dimensional structures and
their potential function in the optical path.
Since the retina in the tree shrews is defined as all-cone
retina with less than 5 per cent rods [4], several concerns
about the unsatisfactory function of such all-cone retina
arise. Firstly, the maximum diameter of the inner segments of the cones of Tupaia is much wider than the
diameter of the outer segments. Therefore, the outer segments are not densely packed, as in the retina of most
mammals that is rich in rods, but rather widely spaced.
As a matter of fact, the cut surface of the outer segment
is only about one-quarter to one-third of the inner segments. Secondly, the epithelial cytoplasmic extensions
Interface Focus (2012)
rich in melanin pigments are projecting deeply into the
spaces between cone photoreceptors (figure 1a). This
means that a considerable percentage of the light penetrating the inner segment would miss the receptors in
the outer segment and rather be absorbed by melanin
pigments, if the light were not refracted strongly towards
the central longitudinal axis of the outer segment.
Thirdly, mammalian pupil constriction is controlled
through rod–rod appositions in the peripheral retina.
As retina of Tupaia has a limited number of rods compared with higher primates, the wavelength limit of the
visual response of a retina rich in rod cells might be shifted
towards the biologically damaging UV region in retina
that is rich in cone cells. Since blue wavelength controls
pupillary constriction, a broader range of wavelengths
extending into the UV-A region (i.e. wavelengths shorter
than 400 nm extending to 320 nm) would be allowed to
enter the eyes. Although the melanin present in the pigment epithelial layer absorbs UV close to the visible
spectral wavelengths (the extinction coefficient of eumelanin is about 20 cm2 mg21 at 400 nm) [8], other protective
mechanisms against overexposure to shorter wavelengths
of UV might be required for a retina of Tupaia that is
devoid of rod photoreceptors. The experimental measurement of the spectra absorbance of Tupaia retina shows a
significant absorbance within the UV range, with peak
absorption/sensitivity close to 420 nm [9]. As such, a ‘curious photostable pigment’ was suggested in the inner
segment of Tupaia retina close to the base of the outer segment [9] to protect the inner segment from UV damage.
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Cubic lens mitochondria Z. Almsherqi et al.
However, the nature and the characteristics of the
pigment have not been identified yet.
Owing to the above-mentioned unsatisfactory conditions, it has been proposed that the unique size, dense
matrix and specialized multi-lamellar system of cristae
of the highly refractive MG of Tupaia might have accessory optical functions to optimize the all cone retina
function. The main proposed function for these MG
is to act as microlenses to enhance the photon capture
of the outer segments [7] and, accordingly, they were
named as ‘lens mitochondria’. However, the foremost
drawback in characterizing their optical function theoretically and experimentally is perhaps owing to the lack
of knowledge about their physical structure. Indeed,
identifying the three-dimensional structure of these
mitochondria is the key to investigate their potential
optical role in the photoreceptors.
2. METHODS
2.1. Identifying three-dimensional structure of
lens mitochondria
A simple yet reliable method for identifying the
three-dimensional configuration of highly convoluted
and complicated structures with cubic symmetry in
TEM images has been developed [10– 13]. Briefly, a
theoretical two-dimensional projection map is computer-generated from a mathematical three-dimensional
model and matched to a TEM micrograph of interest.
From this template-matching process, theoretical conclusions about the three-dimensional definition and
shape are drawn. This procedure is known as direct template-matching method and is mainly based on pattern
recognition [10,11,13]. The reliability of this method
in predicting the three-dimensional cubic membrane
structure as inferred from two-dimensional TEM
images has been further evaluated and confirmed by
the three-dimensional reconstruction technique of
electron tomography [2].
2.2. Three-dimensional simulator for light
transport across multi-layer cubic
membranes
As both lens mitochondria and three-dimensional
photonic crystals share the same geometry (gyroid), it
is interesting to speculate that cubic membrane architecture in the lens mitochondria of tree shrew may act as a
nanolens to focus light at the narrow outer segment.
More importantly, it may function as a three-dimensional
biophotonic crystal with a lattice size close to UV wavelength; thus, its optical property might be able to block
or direct UV light away from reaching the outer segment
of cone photoreceptors. The multi-layer gyroid-surfacebased cubic membrane arrangement of lens mitochondria
in Tupaia photoreceptors may enable the mitochondria to
amplify, filter or re-direct selectively certain wavelengths
of light, while discriminating other wavelength ranges.
To explore the presumed optical properties of the lens
mitochondria beyond light collection and focusing, we
programmed a simplified model of the lipid membrane
layers that tessellate the volume of the mitochondrion.
The dimension of the layers within each membrane is of
Interface Focus (2012)
541
the same magnitude as optical coatings for anti-reflecting
surfaces or interference filters. As the refractive indices
(RIs) of all the lipids and interstitial spaces within the
biological membrane are known [14,15], the membrane
can be modelled as special case of a stratified medium
[16], where the layers have constant thickness but are
strongly spatially curved.
We tested two paradigms (different models) for the
simulator setup: (i) the transport of spherical waves
across the unit cell of the cubic membrane where all the
input and output light is described in terms of monochromatic spherical waves travelling into and out of the unit
cell. The other setup is a (ii) modified Monte Carlo simulator in which rays carry the energy and the phase of the
light. Upon traversing an interface, the ray splits into a
forward and a reflected portion (or optionally into several
forward portions to account for higher orders of diffraction). Upon leaving the confinement sphere, the
amplitudes and phases are integrated on the image
planes and then finally merged. As we are less interested
in the proper shape of the resulting focal regions rather
than in the energy transmitted through such a system,
we implemented both versions for our simulation study
(for details refer to Xu et al. [17]).
3. RESULTS AND DISCUSSION
3.1. ‘Lens mitochondria’ with multi-layer gyroidbased cubic membrane arrangement
We have previously identified complex gyroid membrane organization with six pairs (12 layers) in the
retina of Tupaia belangeri [3]. In this report, we use a
published TEM micrograph of a lens mitochondrion
of Tupaia glis photoreceptors [4] to define the type of
inner membrane arrangements by using the abovementioned template-matching method. The TEM micrograph of interest (patterned membranes) is shown in
figure 1a. The first step is the pattern recognition by
eye through looking into our collected two-dimensional
projection library followed by matching the density
details through modifying the parameters such as
number of membranes, section thickness and viewing
directions [11,13]. Each type of cubic membrane has
its own unique patterned signature, and this becomes evident when the gyroid configuration is extrapolated to its
TEM two-dimensional counter form (figure 1c). After
careful inspection and evaluation, the order membrane
domain appears to be of a multi-layer (8–12 layers)
gyroid-based cubic membrane arrangement (figure 1).
As shown in figure 1a, the inner membrane cristae
of lens mitochondria have 8 – 12 parallel and closely
packed gyroid-surface cubic membrane arrangements.
The estimated lattice size of this complicated multilayer cubic membrane structure is about 400 nm. To
the best of our knowledge, this mitochondrial inner
membrane organization represents the highest number
of multi-layer cubic membrane structures reported in biological systems. In most of the observed cubic membranes,
the membranous structure consists of either a single
membrane or, more commonly, one pair of parallel
membranes [3]. Similar structures, however, have been
generated and extensively studied in surfactant and
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Cubic lens mitochondria Z. Almsherqi et al.
(a)
retina
light
(b)
optic nerve cells
cone photoreceptor
pigment epithelium
choroid
sclera
(c)
pigment
UV
blue focus
green focus
red focus
cubic lens mitochondrion
UV
inner segment
outer segment
Figure 2. Schematic of the all-cone retina in the eye of tree shrew (Tupaia glis). (a) A simplified cross section of an eye; (b) level of
sensor cells in the retina layer; (c) inner segment containing a large cubic mitochondrion adjacent to a couple of smaller mitochondria. Multi-focal points of red, green and blue wavelengths; UV may be rejected backward in the outer segment based on
the quasi-photonic properties of the cubic membrane arrangement in lens mitochondria. Arrows indicate cubic membrane
orientation and contact across the mitochondria supporting waveguide properties of multi-layer cubic membrane arrangement.
water–lipid systems [18,19]. The significance of these
multi-layer cubic membrane arrangements might be
correlated with amplification, multiplication or fine
manipulation of the proposed function. The tree shrew’s
‘lens mitochondria’ morphology is based on a multilayer gyroid-based cubic membrane arrangement. The
apparent three-dimensional geometric similarity between
these unique ‘lens mitochondria’ and three-dimensional
photonic crystals may spark more interest in investigating
and understanding potential functions of these intriguing
membrane arrangements in living systems.
3.2. Optical properties of multi-layer gyroidbased cubic membrane arrangements
The photonic properties of cubic phases based on triply
periodic-level surfaces (gyroid, G; double diamond, D; and
primitive, P) have been studied theoretically [20–22]
and experimentally [23,24]. The same G-surfaces are
used to describe cubic membrane organization of lens
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mitochondria in this report. In general, the lattice size
of the photonic crystal has to be equal to the wavelength
of the light or electromagnetic wave that one wants to
manipulate. Three-dimensional simulation data show
that the unique 12-layer gyroid cubic membrane
arrangements observed in the retina of tree shrew may
act as multi-focal lens, angle-independent interference
filters that disperse short waves including UV light,
and waveguide photonic crystal as well (for details see
Xu et al. [17]).
3.2.1. Photon focus and dispersion
The three-dimensional simulation data [17] show that
MG with cubic membrane organization is able to
focus the incident light at different focal points. The
shift of the geometric focus is dependent on the wavelength. The short waves are focused in close proximity
to cubic MG, while the long waves are focused far from
the MG (figure 2). All the focal points are located
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Cubic lens mitochondria Z. Almsherqi et al.
within the long axis of the folded membrane in the
outer segment of the retina. However, for wavelengths
approaching 800 nm (twice the lattice constant), the
geometric focus is lost or nearly lost.
Multi-focal capacity of MG may enhance colour perception of the tree shrew animals. It is well known that
tree shrews are diurnal animals, with voracious appetites and unusually high metabolic rates. Shrews may
consume food up to 80 –90% of their own body weight
daily. Without trichromacy ability, the tree shrews
would share the difficulty of the mammalian dichromat
in detecting ripe fruit against the dappled background
of forest foliage [25,26]. It is primarily at wavelengths
above 500 nm that the spectral reflectance curves of
yellow or orange fruit differ from those of background
leaves [27]. Thus, the dichromatic consumer can seldomly detect such fruit by colour, since the colour
vision depends on their short-wave cones, which
absorb negligibly above 500 nm.
Interestingly, we also found that light of wavelengths above 650 nm yield second, elongate, region in
depth where the light is relatively focused (second
focus), but only for the range around twofold lattice constant; the power flux in the second focus
exceeds the one in the (lost) focal region. The biological significance of this second focus region is
currently unknown.
3.2.2. Interference filter
The striking similarity between the three-dimensional
arrangement of ‘lens mitochondria’ inner membranes
and certain experimentally produced photonic crystals
with photonic bandgap (PBG) or wave guidance is
obvious [20,28]. Photonic crystals are periodic dielectric
composite nanostructures that are designed to affect the
propagation of electromagnetic waves in the same way
as the periodic potential in a semiconductor crystal
affects the electron motion by defining allowed and
forbidden electronic energy bands [29]. The simplest
form of a photonic crystal is a one-dimensional periodic structure, such as a multi-layer film. A photonic
crystal with hexagonal lattice represents a typical
two-dimensional photonic crystal. However, strong
confinement (or control) of photons can be possible
by using three-dimensional periodic crystals with
corresponding three-dimensional PBG that forbid
propagation of light waves, in any direction and for
any polarization, for a certain frequency range. As
both lens mitochondria and photonic crystals with
PBG properties share the same geometry (gyroid
type), it is tempting to speculate that cubic membrane architecture in the lens mitochondria of Tupaia
species may function as a photonic crystal with a lattice
size close to UV wavelength, and that their PBG property might be able to block or direct UV light from
reaching the outer segment of photoreceptors in the
rod-deficient retina.
Our work on simulating the light transport through
the multi-layer cubic membrane arrangement shows
that photonic crystal properties might not be required
for the lens mitochondria to operate as a wide-angle,
broad-band UV filter in front of the outer segment of
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the photoreceptors. Our simulations ascribe to a simplified assembly of such membranes the power to reduce
UV transmission by as much as 50 per cent by dispersing
the UV light. We were not able to identify a definitive
focus point for the wavelengths less than 400 nm or
more than 800 nm. The interference filters also show sufficiently steep transitions not to block the visible light
from the eye (figure 2). MG with cubic membrane
arrangement may not act as a perfect quasi-photonic
crystal maybe because the changes in refractive index
are too small and the lipid-bilayer-based membrane
(approx. 5 nm) is too narrow to create bandgaps; however, it works as a decently effective bandpass that
suppresses a majority of the short wavelengths
yet allows the longer wavelengths to be transported
much more efficiently through a multi-layer cubic membrane arrangement. Furthermore, our simulation data
may explain the experimental results which show the
ability of Tupaia retina to prevent the transmission of
near-blue and UV light to the outer segment [9].
3.2.3. Waveguide properties
The TEM images often show that an apical MG is
usually placed on top of three to six closely packed
MG. Together, the MG form a solid mass that fills
the conical upper region of the inner segment. Multiple
contact points are also observed between the densely
packed MG (figure 2). Furthermore, cubic membrane
orientation seems to be maintained across the adjacent
MG (figure 1a). These observations in the published
TEM images may suggest that MG with cubic membrane arrangement might have waveguide properties
to direct the light from the inner mitochondrial layer
towards the apical MG where the light might be further
focused on the narrow outer segment. Our threedimensional simulation data support this notion and,
as expected, the two separate compartments of the
MG with different RIs, the channels inside the compartment with the higher RI, form a mild waveguide that
preferentially propagates light inside that compartment
(figure 3). The capturing angle for light into these channels is astonishingly large and the efficiency of the
waveguide transport increases with the wavelength of
the light (figure 3).
4. CONCLUSIONS
Previous studies suggested that membrane-bound ‘ellipsosomes’, lipid droplets and MG [7] might play a role in
altering the spectral sensitivity of the photoreceptors to
act as microlenses to enhance the photon capture in the
outer segment of the photoreceptors. Apparently, cubic
membrane structures are linked to light reactive biomembranes in plant tissues as well, such as the cubic
structures found in the green algae Zygnema chloroplasts and in the prolamellar body (PLB) of
photosynthetic cells in higher plants [3]. A physical
role has been proposed for the selection of D-surface
geometry [30], based on theoretical considerations on
how the geometry of crystals controls the emission or
absorption of certain wavelengths of light through the
existence of photonic bandgaps [20]. Although the
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Cubic lens mitochondria Z. Almsherqi et al.
5 mm
l = 350 nm
l = 400 nm
l = 600 nm
l = 800 nm
Figure 3. Three-dimensional simulation plot of the intensity patterns for various wavelengths of light as they are transmitted
through a ‘lens mitochondrion’ with a multi-layer gyroid-based cubic membrane arrangement. After leaving the mitochondrion,
the light leaves the pattern illustrated in the figure. The vertical axis is the distance from the mitochondrion and the shape of the
blob is a surface of constant intensity (constant power flux). The images are projections from the three-dimensional distribution
without perspective distortion and are hence to scale in all axes. The total power of the transmission increases dramatically for
longer wavelengths but focus and bundling and hence the peak intensity is higher for shorter wavelengths. Marked by red arrows
is the emission from waveguides created by straight single-compartment channels inside the mitochondrion present for all wavelengths examined. The shape of this light emission ‘blob’ including the waveguide peaks strongly depends on the orientation of
the mitochondrion and polarization of the light. The mitochondrion exhibits an overly simple and imperfect photonic bandgap
which is achieved despite very low changes of refractive indices in the membranes.
D-surface is isotropic, its geometry is such that it may
potentially trap photons. The absorbed energy could
then be used by certain molecules that are positioned
along a particular lattice direction, and, for instance,
trigger conformational changes to transform PLB into
an active thylakoid membrane geometry. A similar
structural role can be considered for the selection of
different subtypes of cubic membrane architectures
( photosome) in bioluminescent scale worms [31,32].
Interestingly, the photosome membrane organization
has a D subtype cubic membrane in the resting, unstimulated state; however, upon electrical or optical
stimulation, the membrane configuration changes and
acquires a P subtype. This suggests that different cubic
membrane subtypes indeed respond to, or manipulate
different wavelengths of light. This also raises the possibility that cubic membranes change their geometrical
configuration upon interaction with light. These questions
clearly deserve further investigation. In this report,
we have shown that the MG, categorized as ‘lens
mitochondria’, are indeed ‘cubic mitochondria’ from
the ultrastructural point of view. The apparent threedimensional ultrastructural similarity of lens (cubic)
mitochondria to photonic crystals and our computational
simulation results strongly suggest a role of cubic
membranes as ‘optical filters’. Our three-dimensional
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simulation of the light transport across the cubic membranes in lens mitochondria further suggests multiple
roles for MG: they may act as: (i) multi-focal lens;
(ii) angle-independent interference filters to block UV
light; and (iii) waveguide photonic crystal. Experimental
investigations are necessary to further test this hypothesis.
We thank Sepp D. Kohlwein for critical reading of the
manuscript. We also thank Mark Mieczkowski for the ‘Cubic
membrane simulation projection’ programme (QMSP) and
Aikkia Khaw for his artwork presented in figure 2.
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